Self inductance of solenoid is

The magnetic potential energy stored in a certain inductor is $$25 \mathrm{~mJ}$$, when the current in the inductor is $$50 \mathrm{~mA}$$. This inductor is of inductance

A wire of length '$$L$$'; having resistance '$$R$$' falls from a height '$$\ell$$' in earth's horizontal magnetic field '$$B$$'. The current through the wire is ( $$\mathrm{g}=$$ acceleration due to gravity)

A coil of radius '$$\mathrm{r}$$' is placed on another coil (whose radius is '$$\mathrm{R}$$' and current through it is changing) so that their centres coincide. ( $$R > r$$ ). If both coplanar, then the mutual inductance between them is proportional to